Evolution on the Biophysical Fitness Landscape of an RNA Virus

Viral evolutionary pathways are determined by the fitness landscape, which maps viral genotype to fitness. However, a quantitative description of the landscape and the evolutionary forces on it remain elusive. Here, we apply a biophysical fitness model based on capsid folding stability and antibody binding affinity to predict the evolutionary pathway of norovirus escaping a neutralizing antibody. The model is validated by experimental evolution in bulk culture and in a drop-based microfluidics that propagates millions of independent small viral subpopulations. We demonstrate that along the axis of binding affinity, selection for escape variants and drift due to random mutations have the same direction, an atypical case in evolution. However, along folding stability, selection and drift are opposing forces whose balance is tuned by viral population size. Our results demonstrate that predictable epistatic tradeoffs between molecular traits of viral proteins shape viral evolution.

Chimeric dihydrofolate reductases display properties of modularity and biophysical diversity

While reverse genetics and functional genomics have long affirmed the role of individual mutations in determining protein function, there have been fewer studies addressing how large-scale changes in protein sequences, such as in entire modular segments, influence protein function and evolution. Given how recombination can reassort protein sequences, these types of changes may play an underappreciated role in how novel protein functions evolve in nature. Such studies could aid our understanding of whether certain organismal phenotypes related to protein function-such as growth in the presence or absence of an antibiotic-are robust with respect to the identity of certain modular segments. In this study, we combine molecular genetics with biochemical and biophysical methods to gain a better understanding of protein modularity in dihydrofolate reductase (DHFR), an enzyme target of antibiotics also widely used as a model for protein evolution. We replace an integral α-helical segment of Escherichia coli DHFR with segments from a number of different organisms (many nonmicrobial) and examine how these chimeric enzymes affect organismal phenotypes (e.g., resistance to an antibiotic) as well as biophysical properties of the enzyme (e.g., thermostability). We find that organismal phenotypes and enzyme properties are highly sensitive to the identity of DHFR modules, and that this chimeric approach can create enzymes with diverse biophysical characteristics.

Mutation rate variability as a driving force in adaptive evolution

Mutation rate is a key determinant of the pace as well as outcome of evolution, and variability in this rate has been shown in different scenarios to play a key role in evolutionary adaptation and resistance evolution under stress caused by selective pressure. Here we investigate the dynamics of resistance fixation in a bacterial population with variable mutation rates, and we show that evolutionary outcomes are most sensitive to mutation rate variations when the population is subject to environmental and demographic conditions that suppress the evolutionary advantage of high-fitness subpopulations. By directly mapping a biophysical fitness function to the system-level dynamics of the population, we show that both low and very high, but not intermediate, levels of stress in the form of an antibiotic result in a disproportionate effect of hypermutation on resistance fixation. We demonstrate how this behavior is directly tied to the extent of genetic hitchhiking in the system, the propagation of high-mutation rate cells through association with high-fitness mutations. Our results indicate a substantial role for mutation rate flexibility in the evolution of antibiotic resistance under conditions that present a weak advantage over wildtype to resistant cells.

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection

Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple life-history traits to selection is a critical question for evolutionary biology as we seek to predict the evolutionary fates of mutations. Here we use a model of microbial growth to show that there are two distinct components of selection corresponding to the growth and lag phases, while the yield modulates their relative importance. The model predicts rich population dynamics when there are trade-offs between phases: multiple strains can coexist or exhibit bistability due to frequency-dependent selection, and strains can engage in rock-paper-scissors interactions due to non-transitive selection. We characterize the environmental conditions and patterns of traits necessary to realize these phenomena, which we show to be readily accessible to experiments. Our results provide a theoretical framework for analysing high-throughput measurements of microbial growth traits, especially interpreting the pleiotropy and correlations between traits across mutants. This work also highlights the need for more comprehensive measurements of selection in simple microbial systems, where the concept of an ordinary fitness landscape breaks down.

ProteomeVis: a web app for exploration of protein properties from structure to sequence evolution across organisms' proteomes

Motivation

Protein evolution spans time scales and its effects span the length of an organism. A web app named ProteomeVis is developed to provide a comprehensive view of protein evolution in the Saccharomyces cerevisiae and Escherichia coli proteomes. ProteomeVis interactively creates protein chain graphs, where edges between nodes represent structure and sequence similarities within user-defined ranges, to study the long time scale effects of protein structure evolution. The short time scale effects of protein sequence evolution are studied by sequence evolutionary rate (ER) correlation analyses with protein properties that span from the molecular to the organismal level.

Results

We demonstrate the utility and versatility of ProteomeVis by investigating the distribution of edges per node in organismal protein chain universe graphs (oPCUGs) and putative ER determinants. S.cerevisiae and E.coli oPCUGs are scale-free with scaling constants of 1.79 and 1.56, respectively. Both scaling constants can be explained by a previously reported theoretical model describing protein structure evolution. Protein abundance most strongly correlates with ER among properties in ProteomeVis, with Spearman correlations of -0.49 (P-value < 10-10) and -0.46 (P-value < 10-10) for S.cerevisiae and E.coli, respectively. This result is consistent with previous reports that found protein expression to be the most important ER determinant.

Availability and implementation

ProteomeVis is freely accessible at http://proteomevis.chem.harvard.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Dynamic disulfide exchange in a crystallin protein in the human eye lens promotes cataract-associated aggregation

Increased light scattering in the eye lens due to aggregation of the long-lived lens proteins, crystallins, is the cause of cataract disease. Several mutations in the gene encoding human γD-crystallin (HγD) cause misfolding and aggregation. Cataract-associated substitutions at Trp⁴² cause the protein to aggregate in vitro from a partially unfolded intermediate locked by an internal disulfide bridge, and proteomic evidence suggests a similar aggregation precursor is involved in age-onset cataract. Surprisingly, WT HγD can promote aggregation of the W42Q variant while itself remaining soluble. Here, a search for a biochemical mechanism for this interaction has revealed a previously unknown oxidoreductase activity in HγD. Using in vitro oxidation, mutational analysis, cysteine labeling, and MS, we have assigned this activity to a redox-active internal disulfide bond that is dynamically exchanged among HγD molecules. The W42Q variant acts as a disulfide sink, reducing oxidized WT and forming a distinct internal disulfide that kinetically traps the aggregation-prone intermediate. Our findings suggest a redox "hot potato" competition among WT and mutant or modified polypeptides wherein variants with the lowest kinetic stability are trapped in aggregation-prone intermediate states upon accepting disulfides from more stable variants. Such reactions may occur in other long-lived proteins that function in oxidizing environments. In these cases, aggregation may be forestalled by inhibiting disulfide flow toward mutant or damaged polypeptides.

Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape

A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.

Accessibility of the Shine-Dalgarno Sequence Dictates N-Terminal Codon Bias in E. coli

Despite considerable efforts, no physical mechanism has been shown to explain N-terminal codon bias in prokaryotic genomes. Using a systematic study of synonymous substitutions in two endogenous E. coli genes, we show that interactions between the coding region and the upstream Shine-Dalgarno (SD) sequence modulate the efficiency of translation initiation, affecting both intracellular mRNA and protein levels due to the inherent coupling of transcription and translation in E. coli. We further demonstrate that far-downstream mutations can also modulate mRNA levels by occluding the SD sequence through the formation of non-equilibrium secondary structures. By contrast, a non-endogenous RNA polymerase that decouples transcription and translation largely alleviates the effects of synonymous substitutions on mRNA levels. Finally, a complementary statistical analysis of the E. coli genome specifically implicates avoidance of intra-molecular base pairing with the SD sequence. Our results provide general physical insights into the coding-level features that optimize protein expression in prokaryotes.

Absence of Selection for Quantum Coherence in the Fenna-Matthews-Olson Complex: A Combined Evolutionary and Excitonic Study

We present a study on the evolution of the Fenna-Matthews-Olson bacterial photosynthetic pigment-protein complex. This protein complex functions as an antenna. It transports absorbed photons-excitons-to a reaction center where photosynthetic reactions initiate. The efficiency of exciton transport is therefore fundamental for the photosynthetic bacterium's survival. We have reconstructed an ancestor of the complex to establish whether coherence in the exciton transport was selected for or optimized over time. We have also investigated the role of optimizing free energy variation upon folding in evolution. We studied whether mutations which connect the ancestor to current day species were stabilizing or destabilizing from a thermodynamic viewpoint. From this study, we established that most of these mutations were thermodynamically neutral. Furthermore, we did not see a large change in exciton transport efficiency or coherence, and thus our results predict that exciton coherence was not specifically selected for.

Structure-Based Prediction of Protein-Folding Transition Paths

We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each transient state corresponds to the assembly of one or more discrete, cooperative units, which are determined directly from the native structure. We show that the transition state on a folding pathway is reached when a small number of critical contacts are formed between a specific set of substructures, after which folding proceeds downhill in free energy. This approach suggests a natural resolution for distinguishing parallel folding pathways and provides a simple means to predict the rate-limiting step in a folding reaction. Our theory identifies a common folding mechanism for proteins with diverse native structures and establishes general principles for the self-assembly of polymers with specific interactions.

Effect of sampling on BACE-1 ligands binding free energy predictions via MM-PBSA calculations

The BACE-1 enzyme is a prime target to find a cure to Alzheimer's disease. In this article, we used the MM-PBSA approach to compute the binding free energies of 46 reported ligands to this enzyme. After showing that the most probable protonation state of the catalytic dyad is mono-protonated (on ASP32), we performed a thorough analysis of the parameters influencing the sampling of the conformational space (in total, more than 35 μs of simulations were performed). We show that ten simulations of 2 ns gives better results than one of 50 ns. We also investigated the influence of the protein force field, the water model, the periodic boundary conditions artifacts (box size), as well as the ionic strength. Amber03 with TIP3P, a minimal distance of 1.0 nm between the protein and the box edges and a ionic strength of I = 0.2 M provides the optimal correlation with experiments. Overall, when using these parameters, a Pearson correlation coefficient of R = 0.84 (R²  = 0.71) is obtained for the 46 ligands, spanning eight orders of magnitude of K_d (from 0.017 nm to 2000 μM, i.e., from -14.7 to -3.7 kcal/mol), with a ligand size from 22 to 136 atoms (from 138 to 937 g/mol). After a two-parameter fit of the binding affinities for 12 of the ligands, an error of RMSD = 1.7 kcal/mol was obtained for the remaining ligands. © 2017 Wiley Periodicals, Inc.

Optimization of lag phase shapes the evolution of a bacterial enzyme

Mutations provide the variation that drives evolution, yet their effects on fitness remain poorly understood. Here we explore how mutations in the essential enzyme adenylate kinase (Adk) of Escherichia coli affect multiple phases of population growth. We introduce a biophysical fitness landscape for these phases, showing how they depend on molecular and cellular properties of Adk. We find that Adk catalytic capacity in the cell (the product of activity and abundance) is the major determinant of mutational fitness effects. We show that bacterial lag times are at a well-defined optimum with respect to Adk's catalytic capacity, while exponential growth rates are only weakly affected by variation in Adk. Direct pairwise competitions between strains show how environmental conditions modulate the outcome of a competition where growth rates and lag times have a tradeoff, shedding light on the multidimensional nature of fitness and its importance in the evolutionary optimization of enzymes.

Graph's Topology and Free Energy of a Spin Model on the Graph

In this Letter we investigate a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and energetic contributions to the free energy, and find that considering the topology is sufficient to qualitatively compare the free energies of different graph systems at high temperature, even when the energetics are not fully known. This method was applied to the metal lattice system with defects, and we found that it partially explains why point defects are more stable than high-dimensional defects. Given the energetics, we can even quantitatively compare free energies of different graph structures via a closed form of linear graph contributions. The closed form is applied to predict the sequence-space free energy of lattice proteins, which is a key factor determining the designability of a protein structure.

Gene Dosage Experiments in Enterobacteriaceae Using Arabinose-regulated Promoters

This protocol is used to assay the effect of protein over-expression on fitness of E. coli. It is based on a plasmid expression of a protein of interest from an arabinose-regulated pBAD promoter followed by the measurement of the intracellular protein abundance by Western blot along with the measurement of growth parameters of E. coli cell expressing this protein.

Transient protein-protein interactions perturb E. coli metabolome and cause gene dosage toxicity

Gene dosage toxicity (GDT) is an important factor that determines optimal levels of protein abundances, yet its molecular underpinnings remain unknown. Here, we demonstrate that overexpression of DHFR in E. coli causes a toxic metabolic imbalance triggered by interactions with several functionally related enzymes. Though deleterious in the overexpression regime, surprisingly, these interactions are beneficial at physiological concentrations, implying their functional significance in vivo. Moreover, we found that overexpression of orthologous DHFR proteins had minimal effect on all levels of cellular organization - molecular, systems, and phenotypic, in sharp contrast to E. coli DHFR. Dramatic difference of GDT between 'E. coli's self' and 'foreign' proteins suggests the crucial role of evolutionary selection in shaping protein-protein interaction (PPI) networks at the whole proteome level. This study shows how protein overexpression perturbs a dynamic metabolon of weak yet potentially functional PPI, with consequences for the metabolic state of cells and their fitness.

Bridging the physical scales in evolutionary biology: from protein sequence space to fitness of organisms and populations

Bridging the gap between the molecular properties of proteins and organismal/population fitness is essential for understanding evolutionary processes. This task requires the integration of the several physical scales of biological organization, each defined by a distinct set of mechanisms and constraints, into a single unifying model. The molecular scale is dominated by the constraints imposed by the physico-chemical properties of proteins and their substrates, which give rise to trade-offs and epistatic (non-additive) effects of mutations. At the systems scale, biological networks modulate protein expression and can either buffer or enhance the fitness effects of mutations. The population scale is influenced by the mutational input, selection regimes, and stochastic changes affecting the size and structure of populations, which eventually determine the evolutionary fate of mutations. Here, we summarize the recent advances in theory, computer simulations, and experiments that advance our understanding of the links between various physical scales in biology.

An Internal Disulfide Locks a Misfolded Aggregation-prone Intermediate in Cataract-linked Mutants of Human γD-Crystallin

Considerable mechanistic insight has been gained into amyloid aggregation; however, a large number of non-amyloid protein aggregates are considered "amorphous," and in most cases, little is known about their mechanisms. Amorphous aggregation of γ-crystallins in the eye lens causes cataract, a widespread disease of aging. We combined simulations and experiments to study the mechanism of aggregation of two γD-crystallin mutants, W42R and W42Q: the former a congenital cataract mutation, and the latter a mimic of age-related oxidative damage. We found that formation of an internal disulfide was necessary and sufficient for aggregation under physiological conditions. Two-chain all-atom simulations predicted that one non-native disulfide in particular, between Cys(32) and Cys(41), was likely to stabilize an unfolding intermediate prone to intermolecular interactions. Mass spectrometry and mutagenesis experiments confirmed the presence of this bond in the aggregates and its necessity for oxidative aggregation under physiological conditions in vitro Mining the simulation data linked formation of this disulfide to extrusion of the N-terminal β-hairpin and rearrangement of the native β-sheet topology. Specific binding between the extruded hairpin and a distal β-sheet, in an intermolecular chain reaction similar to domain swapping, is the most probable mechanism of aggregate propagation.

Evolutionary dynamics of viral escape under antibodies stress: A biophysical model

Viruses constantly face the selection pressure of antibodies, either from innate immune response of the host or from administered antibodies for treatment. We explore the interplay between the biophysical properties of viral proteins and the population and demographic variables in the viral escape. The demographic and population genetics aspect of the viral escape have been explored before; however one important assumption was the a priori distribution of fitness effects (DFE). Here, we relax this assumption by instead considering a realistic biophysics-based genotype-phenotype relationship for RNA viruses escaping antibodies stress. In this model the DFE is itself an evolvable property that depends on the genetic background (epistasis) and the distribution of biophysical effects of mutations, which is informed by biochemical experiments and theoretical calculations in protein engineering. We quantitatively explore in silico the viability of viral populations under antibodies pressure and derive the phase diagram that defines the fate of the virus population (extinction or escape from stress) in a range of viral mutation rates and antibodies concentrations. We find that viruses are most resistant to stress at an optimal mutation rate (OMR) determined by the competition between supply of beneficial mutation to facilitate escape from stressors and lethal mutagenesis caused by excess of destabilizing mutations. We then show the quantitative dependence of the OMR on genome length and viral burst size. We also recapitulate the experimental observation that viruses with longer genomes have smaller mutation rate per nucleotide.

A Simple Model of Protein Domain Swapping in Crowded Cellular Environments

Domain swapping in proteins is an important mechanism of functional and structural innovation. However, despite its ubiquity and importance, the physical mechanisms that lead to domain swapping are poorly understood. Here, we present a simple two-dimensional coarse-grained model of protein domain swapping in the cytoplasm. In our model, two-domain proteins partially unfold and diffuse in continuous space. Monte Carlo multiprotein simulations of the model reveal that domain swapping occurs at intermediate temperatures, whereas folded dimers and folded monomers prevail at low temperatures, and partially unfolded monomers predominate at high temperatures. We use a simplified amino acid alphabet consisting of four residue types, and find that the oligomeric state at a given temperature depends on the sequence of the protein. We also show that hinge strain between domains can promote domain swapping, consistent with experimental observations for real proteins. Domain swapping depends nonmonotonically on the protein concentration, with domain-swapped dimers occurring at intermediate concentrations and nonspecific interactions between partially unfolded proteins occurring at high concentrations. For folded proteins, we recover the result obtained in three-dimensional lattice simulations, i.e., that functional dimerization is most prevalent at intermediate temperatures and nonspecific interactions increase at low temperatures.

Minimalistic predictor of protein binding energy: contribution of solvation factor to protein binding

It has long been known that solvation plays an important role in protein-protein interactions. Here, we use a minimalistic solvation-based model for predicting protein binding energy to estimate quantitatively the contribution of the solvation factor in protein binding. The factor is described by a simple linear combination of buried surface areas according to amino-acid types. Even without structural optimization, our minimalistic model demonstrates a predictive power comparable to more complex methods, making the proposed approach the basis for high throughput applications. Application of the model to a proteomic database shows that receptor-substrate complexes involved in signaling have lower affinities than enzyme-inhibitor and antibody-antigen complexes, and they differ by chemical compositions on interfaces. Also, we found that protein complexes with components that come from the same genes generally have lower affinities than complexes formed by proteins from different genes, but in this case the difference originates from different interface areas. The model was implemented in the software PYTHON, and the source code can be found on the Shakhnovich group webpage: http://faculty.chemistry.harvard.edu/shakhnovich/software.